where \(b_i(S)\)  denotes the \(i\) -th Betti number that counts the number of \((i+1)\) -dimensional holes in \(S\) . The Betti number is generally used to distinguish between spaces with different characteristics in algebraic topology [1]}. \(S\)  contains instances positively classified by the network \(\mathcal {N}\) . Therefore, \(B(S)\)  can be used to investigate how \(S\)  is affected by the architecture of \(\mathcal {N}\)  and can represent the model complexity.
